organ =
read_csv("./data/organ.csv") %>%
filter(county != "TOTAL NYS") ## Parsed with column specification:
## cols(
## pop_2012 = col_integer(),
## chart_month = col_character(),
## county = col_character(),
## eligible_population_enrolled = col_double(),
## location = col_character(),
## month = col_integer(),
## opo = col_character(),
## population_18_estimate = col_integer(),
## registry_enrollments = col_integer(),
## year = col_integer(),
## dummy_day = col_character(),
## date = col_date(format = "")
## )demo_ny =
read.csv("./data/ahrf_select_data.csv") %>% as.tibble() %>%
janitor::clean_names() %>%
rename(county = county_name) Note that there is a sudden leap in registry enrollments at 2017-10-1:
county_enrollment_plot =
organ %>%
ggplot(aes(x = date, y = registry_enrollments, color = county)) +
geom_line()
ggplotly(county_enrollment_plot)county_enrollment_rate_plot =
organ %>%
ggplot(aes(x = date, y = eligible_population_enrolled, color = county)) +
geom_line()
ggplotly(county_enrollment_rate_plot)population_enrollment_plot =
organ %>%
ggplot(aes(y = registry_enrollments, x = population_18_estimate, color = county)) +
geom_point()
ggplotly(population_enrollment_plot)# There was a huge leap in pupulation_18_estimate at 2017-10-01 among almost all the counties
organ %>%
# only use data after 2017-10-01
filter(date > '2017-10-01') %>%
mutate(text_label = str_c("Eligible pop:", population_18_estimate, '\nregistry_enrollments: ', registry_enrollments, "\nCounty:", county, "\ndate:", date)) %>%
plot_ly(x = ~population_18_estimate, y = ~registry_enrollments, type = "scatter", mode = "markers",
#alpha = 0.5,
color = ~county,
text = ~text_label)## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors
## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors# use the data of Sep 2018
organ_2018_sep =
=======
To fit a regression model, use the data of Sep 2018 only.
organ_2018_sep =
>>>>>>> 552cbca9b4d51bf3aa73d83ff51f914f9fa736e7
organ %>%
filter(date > '2017-10-01') %>%
filter(month == 9)
fit = lm(registry_enrollments ~ population_18_estimate, data = organ_2018_sep)
organ_2018_sep %>%
mutate(text_label = str_c("Eligible pop:", population_18_estimate, '\nregistry_enrollments: ', registry_enrollments, "\nCounty:", county, "\ndate:", date)) %>%
plot_ly(x = ~population_18_estimate, y = ~registry_enrollments, mode = "markers") %>%
add_markers(y = ~registry_enrollments) %>%
add_trace(x = ~population_18_estimate, y = fitted(fit), mode = "lines") %>%
layout(showlegend = F)
## No trace type specified:
## Based on info supplied, a 'scatter' trace seems appropriate.
## Read more about this trace type -> https://plot.ly/r/reference/#scatter
<<<<<<< HEAD
=======
>>>>>>> 552cbca9b4d51bf3aa73d83ff51f914f9fa736e7
This plot doesn’t show much information.
organ_df_sep =
organ %>%
group_by(county, year) %>%
arrange(county, date) %>%
mutate(prop_reg_enroll = registry_enrollments / population_18_estimate)
organ_df_sep %>%
ggplot(aes(x = year, y = prop_reg_enroll, group = county, color = county)) +
geom_line()
variables_list = read_csv("./data/ahrf_selected_variables.csv")$label## Parsed with column specification:
## cols(
## label = col_character(),
## topic = col_character()
## )regression_df =
inner_join(by = 'county', organ_2018_sep, demo_ny) %>%
select(opo, population_18_estimate, registry_enrollments, eligible_population_enrolled,
standardzd_per_capita_medcr_cost_fee_for_service_2015:percent_educ_hlth_care_soc_asst_2011_15) %>%
<<<<<<< HEAD
mutate(opo = as.factor(opo)) %>%
mutate(pop_total_2015 = pop_total_female_2015 + pop_total_male_2015,
male_proportion_2015 = pop_total_male_2015 / pop_total_2015,
white_proportion_2015 = (pop_white_female_2015 + pop_white_male_2015) / pop_total_2015,
black_proportion_2015 = (pop_black_african_amer_female_2015 + pop_black_african_amer_male_2015) / pop_total_2015
)
plot =
regression_df %>%
ggplot(aes(y = registry_enrollments, x = pop_total_2015)) +
geom_point()
ggplotly(plot)# medicare enrollment is strongly associated with donor registration rate
regression_df %>%
lm(registry_enrollments ~ population_18_estimate + pop_total_2015 * medicare_enrollment_aged_tot_2015 + x_persons_25_w_4_yrs_college_2011_15+ male_proportion_2015 + white_proportion_2015 + black_proportion_2015 + percent_educ_hlth_care_soc_asst_2011_15 + opo , data = .) %>% # broom::tidy()
summary()##
## Call:
## lm(formula = registry_enrollments ~ population_18_estimate +
## pop_total_2015 * medicare_enrollment_aged_tot_2015 + x_persons_25_w_4_yrs_college_2011_15 +
## male_proportion_2015 + white_proportion_2015 + black_proportion_2015 +
## percent_educ_hlth_care_soc_asst_2011_15 + opo, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -68775 -2968 -10 4201 45219
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -7.501e+03 2.028e+05
## population_18_estimate 8.604e-01 1.834e-01
## pop_total_2015 7.794e-01 1.849e-01
## medicare_enrollment_aged_tot_2015 -1.086e+00 2.882e-01
## x_persons_25_w_4_yrs_college_2011_15 7.097e+02 5.570e+02
## male_proportion_2015 2.333e+05 4.211e+05
## white_proportion_2015 -2.202e+05 1.844e+05
## black_proportion_2015 -3.403e+04 3.325e+05
## percent_educ_hlth_care_soc_asst_2011_15 -7.539e+02 8.523e+02
## opoFinger Lakes Donor Recovery Network 5.804e+03 6.175e+03
## opoNew York Organ Donor Network -1.968e+04 1.490e+04
## opoUNYTS 1.173e+04 8.693e+03
## pop_total_2015:medicare_enrollment_aged_tot_2015 -9.604e-09 2.248e-08
## t value Pr(>|t|)
## (Intercept) -0.037 0.970648
## population_18_estimate 4.692 2.36e-05 ***
## pop_total_2015 4.216 0.000112 ***
## medicare_enrollment_aged_tot_2015 -3.768 0.000458 ***
## x_persons_25_w_4_yrs_college_2011_15 1.274 0.208913
## male_proportion_2015 0.554 0.582267
## white_proportion_2015 -1.194 0.238525
## black_proportion_2015 -0.102 0.918904
## percent_educ_hlth_care_soc_asst_2011_15 -0.885 0.380897
## opoFinger Lakes Donor Recovery Network 0.940 0.352083
## opoNew York Organ Donor Network -1.321 0.192942
## opoUNYTS 1.349 0.183740
## pop_total_2015:medicare_enrollment_aged_tot_2015 -0.427 0.671153
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18880 on 47 degrees of freedom
## Multiple R-squared: 0.9826, Adjusted R-squared: 0.9782
## F-statistic: 221.7 on 12 and 47 DF, p-value: < 2.2e-16## Warning: Column `county` joining character vector and factor, coercing into
## character vector# regression_df %>% View
# regression_df %>% strregression_df %>%
select(-opo) %>%
cor()## percent_enrolled
## percent_enrolled 1.00000000
## population_18_estimate -0.63490860
## registry_enrollments -0.49158996
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.71517542
## median_age_2010 0.34454090
## percent_persons_25_w_hs_diploma_2011_15 -0.63120091
## percent_persons_25_w_4_yrs_college_2011_15 -0.16628458
## percent_educ_hlth_care_soc_asst_2011_15 -0.00394551
## pop_total_2015 -0.64393914
## percent_male_2015 0.32319406
## percent_white_2015 0.70400981
## percent_black_2015 -0.68582797
## percent_asian_2015 -0.57600794
## percent_medicare_enrollment_2015 0.51446805
## population_18_estimate
## percent_enrolled -0.63490860
## population_18_estimate 1.00000000
## registry_enrollments 0.94582698
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.69146325
## median_age_2010 -0.41670095
## percent_persons_25_w_hs_diploma_2011_15 0.46307285
## percent_persons_25_w_4_yrs_college_2011_15 0.48888029
## percent_educ_hlth_care_soc_asst_2011_15 -0.06983545
## pop_total_2015 0.99908123
## percent_male_2015 -0.49973737
## percent_white_2015 -0.86726622
## percent_black_2015 0.79371160
## percent_asian_2015 0.80989287
## percent_medicare_enrollment_2015 -0.46814424
## registry_enrollments
## percent_enrolled -0.49158996
## population_18_estimate 0.94582698
## registry_enrollments 1.00000000
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.63491378
## median_age_2010 -0.39008831
## percent_persons_25_w_hs_diploma_2011_15 0.27915137
## percent_persons_25_w_4_yrs_college_2011_15 0.61397806
## percent_educ_hlth_care_soc_asst_2011_15 -0.08077614
## pop_total_2015 0.93857345
## percent_male_2015 -0.51746669
## percent_white_2015 -0.77408127
## percent_black_2015 0.71329807
## percent_asian_2015 0.71166104
## percent_medicare_enrollment_2015 -0.41644654
## standardzd_per_capita_medcr_cost_fee_for_service_2015
## percent_enrolled -0.71517542
## population_18_estimate 0.69146325
## registry_enrollments 0.63491378
## standardzd_per_capita_medcr_cost_fee_for_service_2015 1.00000000
## median_age_2010 -0.29045851
## percent_persons_25_w_hs_diploma_2011_15 0.39235752
## percent_persons_25_w_4_yrs_college_2011_15 0.35055102
## percent_educ_hlth_care_soc_asst_2011_15 -0.08339607
## pop_total_2015 0.70075487
## percent_male_2015 -0.37455895
## percent_white_2015 -0.70612601
## percent_black_2015 0.71811157
## percent_asian_2015 0.52190295
## percent_medicare_enrollment_2015 -0.47386090
## median_age_2010
## percent_enrolled 0.3445409
## population_18_estimate -0.4167010
## registry_enrollments -0.3900883
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.2904585
## median_age_2010 1.0000000
## percent_persons_25_w_hs_diploma_2011_15 -0.2651434
## percent_persons_25_w_4_yrs_college_2011_15 -0.3314566
## percent_educ_hlth_care_soc_asst_2011_15 -0.4463922
## pop_total_2015 -0.4206015
## percent_male_2015 0.2491281
## percent_white_2015 0.5758090
## percent_black_2015 -0.5285397
## percent_asian_2015 -0.4685420
## percent_medicare_enrollment_2015 0.8510414
## percent_persons_25_w_hs_diploma_2011_15
## percent_enrolled -0.63120091
## population_18_estimate 0.46307285
## registry_enrollments 0.27915137
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.39235752
## median_age_2010 -0.26514343
## percent_persons_25_w_hs_diploma_2011_15 1.00000000
## percent_persons_25_w_4_yrs_college_2011_15 -0.30073461
## percent_educ_hlth_care_soc_asst_2011_15 -0.09713816
## pop_total_2015 0.47387774
## percent_male_2015 -0.02960253
## percent_white_2015 -0.56172408
## percent_black_2015 0.63397442
## percent_asian_2015 0.25743312
## percent_medicare_enrollment_2015 -0.33455700
## percent_persons_25_w_4_yrs_college_2011_15
## percent_enrolled -0.1662846
## population_18_estimate 0.4888803
## registry_enrollments 0.6139781
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.3505510
## median_age_2010 -0.3314566
## percent_persons_25_w_hs_diploma_2011_15 -0.3007346
## percent_persons_25_w_4_yrs_college_2011_15 1.0000000
## percent_educ_hlth_care_soc_asst_2011_15 0.2607478
## pop_total_2015 0.4741145
## percent_male_2015 -0.5255911
## percent_white_2015 -0.4751449
## percent_black_2015 0.3545907
## percent_asian_2015 0.5943618
## percent_medicare_enrollment_2015 -0.2574109
## percent_educ_hlth_care_soc_asst_2011_15
## percent_enrolled -0.00394551
## population_18_estimate -0.06983545
## registry_enrollments -0.08077614
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.08339607
## median_age_2010 -0.44639223
## percent_persons_25_w_hs_diploma_2011_15 -0.09713816
## percent_persons_25_w_4_yrs_college_2011_15 0.26074785
## percent_educ_hlth_care_soc_asst_2011_15 1.00000000
## pop_total_2015 -0.06043419
## percent_male_2015 -0.15108991
## percent_white_2015 -0.11954539
## percent_black_2015 0.08104906
## percent_asian_2015 0.10408561
## percent_medicare_enrollment_2015 -0.25301343
## pop_total_2015
## percent_enrolled -0.64393914
## population_18_estimate 0.99908123
## registry_enrollments 0.93857345
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.70075487
## median_age_2010 -0.42060147
## percent_persons_25_w_hs_diploma_2011_15 0.47387774
## percent_persons_25_w_4_yrs_college_2011_15 0.47411452
## percent_educ_hlth_care_soc_asst_2011_15 -0.06043419
## pop_total_2015 1.00000000
## percent_male_2015 -0.49932871
## percent_white_2015 -0.87055919
## percent_black_2015 0.80373659
## percent_asian_2015 0.80057431
## percent_medicare_enrollment_2015 -0.47338872
## percent_male_2015
## percent_enrolled 0.32319406
## population_18_estimate -0.49973737
## registry_enrollments -0.51746669
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.37455895
## median_age_2010 0.24912805
## percent_persons_25_w_hs_diploma_2011_15 -0.02960253
## percent_persons_25_w_4_yrs_college_2011_15 -0.52559114
## percent_educ_hlth_care_soc_asst_2011_15 -0.15108991
## pop_total_2015 -0.49932871
## percent_male_2015 1.00000000
## percent_white_2015 0.45614358
## percent_black_2015 -0.43553012
## percent_asian_2015 -0.44596854
## percent_medicare_enrollment_2015 0.12674505
## percent_white_2015
## percent_enrolled 0.7040098
## population_18_estimate -0.8672662
## registry_enrollments -0.7740813
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.7061260
## median_age_2010 0.5758090
## percent_persons_25_w_hs_diploma_2011_15 -0.5617241
## percent_persons_25_w_4_yrs_college_2011_15 -0.4751449
## percent_educ_hlth_care_soc_asst_2011_15 -0.1195454
## pop_total_2015 -0.8705592
## percent_male_2015 0.4561436
## percent_white_2015 1.0000000
## percent_black_2015 -0.9523469
## percent_asian_2015 -0.8055503
## percent_medicare_enrollment_2015 0.5969293
## percent_black_2015
## percent_enrolled -0.68582797
## population_18_estimate 0.79371160
## registry_enrollments 0.71329807
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.71811157
## median_age_2010 -0.52853969
## percent_persons_25_w_hs_diploma_2011_15 0.63397442
## percent_persons_25_w_4_yrs_college_2011_15 0.35459069
## percent_educ_hlth_care_soc_asst_2011_15 0.08104906
## pop_total_2015 0.80373659
## percent_male_2015 -0.43553012
## percent_white_2015 -0.95234686
## percent_black_2015 1.00000000
## percent_asian_2015 0.60124031
## percent_medicare_enrollment_2015 -0.57056349
## percent_asian_2015
## percent_enrolled -0.5760079
## population_18_estimate 0.8098929
## registry_enrollments 0.7116610
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.5219029
## median_age_2010 -0.4685420
## percent_persons_25_w_hs_diploma_2011_15 0.2574331
## percent_persons_25_w_4_yrs_college_2011_15 0.5943618
## percent_educ_hlth_care_soc_asst_2011_15 0.1040856
## pop_total_2015 0.8005743
## percent_male_2015 -0.4459685
## percent_white_2015 -0.8055503
## percent_black_2015 0.6012403
## percent_asian_2015 1.0000000
## percent_medicare_enrollment_2015 -0.4557122
## percent_medicare_enrollment_2015
## percent_enrolled 0.5144680
## population_18_estimate -0.4681442
## registry_enrollments -0.4164465
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -0.4738609
## median_age_2010 0.8510414
## percent_persons_25_w_hs_diploma_2011_15 -0.3345570
## percent_persons_25_w_4_yrs_college_2011_15 -0.2574109
## percent_educ_hlth_care_soc_asst_2011_15 -0.2530134
## pop_total_2015 -0.4733887
## percent_male_2015 0.1267450
## percent_white_2015 0.5969293
## percent_black_2015 -0.5705635
## percent_asian_2015 -0.4557122
## percent_medicare_enrollment_2015 1.0000000lm(percent_enrolled ~ ., regression_df) %>% summary##
## Call:
## lm(formula = percent_enrolled ~ ., data = regression_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.5463 -2.2341 -0.1135 2.1545 7.2236
##
## Coefficients:
## Estimate
## (Intercept) 6.381e+01
## opoCenter for Donation and Transplant in New York 7.300e+00
## opoFinger Lakes Donor Recovery Network 1.141e+01
## opoUNYTS 1.111e+01
## population_18_estimate 8.188e-05
## registry_enrollments -5.186e-05
## standardzd_per_capita_medcr_cost_fee_for_service_2015 -4.786e-04
## median_age_2010 -8.650e-01
## percent_persons_25_w_hs_diploma_2011_15 -9.051e-01
## percent_persons_25_w_4_yrs_college_2011_15 3.189e-01
## percent_educ_hlth_care_soc_asst_2011_15 -1.975e-01
## pop_total_2015 -4.774e-05
## percent_male_2015 1.114e+00
## percent_white_2015 -5.947e-01
## percent_black_2015 -6.577e-01
## percent_asian_2015 -1.797e+00
## percent_medicare_enrollment_2015 1.375e+00
## Std. Error t value
## (Intercept) 7.061e+01 0.904
## opoCenter for Donation and Transplant in New York 2.773e+00 2.632
## opoFinger Lakes Donor Recovery Network 3.035e+00 3.759
## opoUNYTS 3.541e+00 3.138
## population_18_estimate 6.152e-05 1.331
## registry_enrollments 2.932e-05 -1.769
## standardzd_per_capita_medcr_cost_fee_for_service_2015 1.145e-03 -0.418
## median_age_2010 3.903e-01 -2.216
## percent_persons_25_w_hs_diploma_2011_15 3.773e-01 -2.399
## percent_persons_25_w_4_yrs_college_2011_15 1.742e-01 1.830
## percent_educ_hlth_care_soc_asst_2011_15 2.105e-01 -0.938
## pop_total_2015 4.371e-05 -1.092
## percent_male_2015 4.964e-01 2.245
## percent_white_2015 5.793e-01 -1.027
## percent_black_2015 7.029e-01 -0.936
## percent_asian_2015 7.149e-01 -2.514
## percent_medicare_enrollment_2015 4.511e-01 3.049
## Pr(>|t|)
## (Intercept) 0.37120
## opoCenter for Donation and Transplant in New York 0.01174 *
## opoFinger Lakes Donor Recovery Network 0.00051 ***
## opoUNYTS 0.00307 **
## population_18_estimate 0.19021
## registry_enrollments 0.08400 .
## standardzd_per_capita_medcr_cost_fee_for_service_2015 0.67809
## median_age_2010 0.03202 *
## percent_persons_25_w_hs_diploma_2011_15 0.02086 *
## percent_persons_25_w_4_yrs_college_2011_15 0.07411 .
## percent_educ_hlth_care_soc_asst_2011_15 0.35334
## pop_total_2015 0.28085
## percent_male_2015 0.02999 *
## percent_white_2015 0.31036
## percent_black_2015 0.35462
## percent_asian_2015 0.01576 *
## percent_medicare_enrollment_2015 0.00392 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.835 on 43 degrees of freedom
## Multiple R-squared: 0.8324, Adjusted R-squared: 0.77
## F-statistic: 13.35 on 16 and 43 DF, p-value: 8.456e-12 # use 'New York Organ Donor Network' as the reference group for opo
lm(percent_enrolled ~ opo + percent_medicare_enrollment_2015 + percent_male_2015 + percent_white_2015*percent_persons_25_w_hs_diploma_2011_15 + percent_persons_25_w_4_yrs_college_2011_15, data = regression_df) %>%
summary()##
## Call:
## lm(formula = percent_enrolled ~ opo + percent_medicare_enrollment_2015 +
## percent_male_2015 + percent_white_2015 * percent_persons_25_w_hs_diploma_2011_15 +
## percent_persons_25_w_4_yrs_college_2011_15, data = regression_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2528 -2.5272 0.0803 1.9416 8.1039
##
## Coefficients:
## Estimate
## (Intercept) -1.180e+02
## opoCenter for Donation and Transplant in New York 8.206e+00
## opoFinger Lakes Donor Recovery Network 1.319e+01
## opoUNYTS 1.371e+01
## percent_medicare_enrollment_2015 7.321e-01
## percent_male_2015 1.620e+00
## percent_white_2015 6.608e-01
## percent_persons_25_w_hs_diploma_2011_15 2.156e+00
## percent_persons_25_w_4_yrs_college_2011_15 3.808e-01
## percent_white_2015:percent_persons_25_w_hs_diploma_2011_15 -3.428e-02
## Std. Error
## (Intercept) 2.932e+01
## opoCenter for Donation and Transplant in New York 1.893e+00
## opoFinger Lakes Donor Recovery Network 1.932e+00
## opoUNYTS 2.336e+00
## percent_medicare_enrollment_2015 2.383e-01
## percent_male_2015 4.223e-01
## percent_white_2015 1.625e-01
## percent_persons_25_w_hs_diploma_2011_15 6.586e-01
## percent_persons_25_w_4_yrs_college_2011_15 1.100e-01
## percent_white_2015:percent_persons_25_w_hs_diploma_2011_15 8.028e-03
## t value
## (Intercept) -4.026
## opoCenter for Donation and Transplant in New York 4.334
## opoFinger Lakes Donor Recovery Network 6.830
## opoUNYTS 5.867
## percent_medicare_enrollment_2015 3.072
## percent_male_2015 3.835
## percent_white_2015 4.067
## percent_persons_25_w_hs_diploma_2011_15 3.274
## percent_persons_25_w_4_yrs_college_2011_15 3.463
## percent_white_2015:percent_persons_25_w_hs_diploma_2011_15 -4.270
## Pr(>|t|)
## (Intercept) 0.000193 ***
## opoCenter for Donation and Transplant in New York 7.06e-05 ***
## opoFinger Lakes Donor Recovery Network 1.11e-08 ***
## opoUNYTS 3.52e-07 ***
## percent_medicare_enrollment_2015 0.003434 **
## percent_male_2015 0.000353 ***
## percent_white_2015 0.000169 ***
## percent_persons_25_w_hs_diploma_2011_15 0.001928 **
## percent_persons_25_w_4_yrs_college_2011_15 0.001106 **
## percent_white_2015:percent_persons_25_w_hs_diploma_2011_15 8.72e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.509 on 50 degrees of freedom
## Multiple R-squared: 0.8368, Adjusted R-squared: 0.8075
## F-statistic: 28.49 on 9 and 50 DF, p-value: < 2.2e-16